Markov Chain Music.ipynb

Kernel: Python 3 (Ubuntu Linux)

$$\text{\Huge Markov Chain Music}$$

import numpy as np
import random

def generate_random_array(n):
    out = np.random.rand(n,n)
    for i in np.arange(n):
        out[i] = out[i]/sum(out[i])
    return out.T


def simple_walk_melody(array,start, steps):
    vec = np.array([[0]]*len(array))
    vec[start] = 1
    notes = []
    for i in np.arange(steps):
        vec = np.dot(array,vec)
        new_note = vec.argmax()+1
        notes = notes + [new_note]
    print(notes)

                      # matrix  Tup natural
def simple_walk_harmony(matrix,start,steps):
    out = np.array([[0]*len(matrix)]*steps, dtype = np.float64)
    for i in start:
        out[0][i] = 1/len(start)
    for j in np.arange(1,steps):
        unfiltered = np.dot(matrix,out[j-1])
        temp = []
        for k in start:
            temp = temp + [unfiltered.argmax()]
            unfiltered[unfiltered.argmax()] = 0
        for l in temp:
            out[j][l] = 1/len(start)
    return out*len(start)

$\text{Random Selection By Adjacency Matrix}$

def weighted_random_selection(array):  # randomly selects an index of array weighted by values of the array
    array = array/sum(array)
    r = random.uniform(0, 1)
    j = 0
    while r > sum(array[0:j]):
        j = j + 1
    return j - 1

def note_from_number(number):
    return ['C','C#','D','D#','E','F','F#','G','G#','A','A#','B'][number]

def weighted_walk(matrix, start, steps):
    out = np.array([[0]*len(matrix)]*steps)
    out[0][start] = 1
    for j in np.arange(1,steps):
        choice = weighted_random_selection(np.dot(matrix,out[j-1]))
        out[j][choice] = 1
    notes = ''
    for row in out:
        notes = notes + note_from_number(row.argmax()) + ' '
    return notes

# ANTHONY

                      # c   c#  d   d#  e   f   f#  g   g#  a   a#  b
Anthony   = np.array([[ 0,  0,  0, .4,  0, .5,  0,.25,.18,  0,  0,  1],  # c
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # c#
                      [.3, .9,  0, .3,  0,  0,  0,.25,  0,.23,  0,  0],  # d
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # d#
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # e
                      [.4,  0, .6,  0, .6,  0,  0,  0,  0,  0,  0,  0],  # f
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,.43,.15,  0],  # f#
                      [.3,  0, .4, .3, .2, .5, .9,  0,  0,  0,  0,  0],  # g
                      [ 0, .1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # g#
                      [ 0,  0,  0,  0,  0,  0,  0,.25,.82,  0,  0,  0],  # a
                      [ 0,  0,  0,  0,  0,  0, .1,  0,  0,  0,  0,  0],  # a#
                      [ 0,  0,  0,  0, .2,  0,  0,.25,  0,.34,.85,  0]]) # b

weighted_walk(Anthony,0,50)

'C D F C G A B C D G C G C G C D F C F C D F C F G B C D F G D F C D F C F C F G B C F C G C F G A F# '

# ESTHER

                      # c   c#  d   d#  e   f   f#  g   g#  a   a#  b
esther    = np.array([[.1, .2,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # c
                      [.1, .2, .2,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # c#
                      [.2, .2, .2,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # d
                      [ 0, .2, .2,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # d#
                      [.1,  0, .2,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # e
                      [.1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # f
                      [.1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # f#
                      [.2,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # g
                      [ 0, .2,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # g#
                      [.1,  0, .2,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # a
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # a#
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0]]) # b

weighted_walk(esther,0,50)

# BLANK

                      # c   c#  d   d#  e   f   f#  g   g#  a   a#  b
Blank     = np.array([[ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # c
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # c#
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # d
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # d#
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # e
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # f
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # f#
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # g
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # g#
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # a
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0],  # a#
                      [ 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0]]) # b